TSTP Solution File: SET014+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:33:31 EDT 2023
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 35 ~; 31 |; 16 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 54 (; 49 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f9,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f15,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f29,plain,
? [B,C,D] :
( subset(B,C)
& subset(D,C)
& ~ subset(union(B,D),C) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
( subset(sk0_2,sk0_3)
& subset(sk0_4,sk0_3)
& ~ subset(union(sk0_2,sk0_4),sk0_3) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
subset(sk0_4,sk0_3),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
~ subset(union(sk0_2,sk0_4),sk0_3),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f38,plain,
~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),sk0_3),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f39,plain,
! [X0] :
( ~ subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),X0) ),
inference(resolution,[status(thm)],[f38,f17]) ).
fof(f41,plain,
~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),sk0_4),
inference(resolution,[status(thm)],[f39,f32]) ).
fof(f42,plain,
~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),sk0_2),
inference(resolution,[status(thm)],[f39,f31]) ).
fof(f46,plain,
! [X0] :
( ~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),union(X0,sk0_4))
| member(sk0_0(sk0_3,union(sk0_2,sk0_4)),X0) ),
inference(resolution,[status(thm)],[f41,f10]) ).
fof(f53,plain,
( spl0_0
<=> member(sk0_0(sk0_3,union(sk0_2,sk0_4)),union(sk0_2,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( member(sk0_0(sk0_3,union(sk0_2,sk0_4)),union(sk0_2,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( ~ member(sk0_0(sk0_3,union(sk0_2,sk0_4)),union(sk0_2,sk0_4))
| spl0_0 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f91,plain,
( subset(union(sk0_2,sk0_4),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f55,f18]) ).
fof(f92,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f33]) ).
fof(f93,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f198,plain,
( member(sk0_0(sk0_3,union(sk0_2,sk0_4)),sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f46,f54]) ).
fof(f199,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f42]) ).
fof(f200,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
$false,
inference(sat_refutation,[status(thm)],[f93,f200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:12:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.050995 seconds
% 0.13/0.40 % CPU time: 0.260067 seconds
% 0.13/0.40 % Memory used: 27.164 MB
%------------------------------------------------------------------------------